Ms Millane, 22, went missing from a hostel in Auckland on December 1 and her body was found in the Waitakere Ranges on Sunday.
A 26-year-old man, who cannot be named, has been charged with murder and appeared in an Auckland court on Monday.
Detective Inspector Scott Beard revealed Grace’s body was found “intact” in an area of bush by Scenic Drive, which runs through the hills.
He said officers are now hunting for an Atlas Trade hardwood long handle, round mouth shovel and appealed for anyone who may have found it after December 3 to come forward.
“At this point we don't know where this item is,” said Mr Beard.
“It could be anywhere between the Scenic Drive and central Auckland areas.
"Someone may have come across it, picked it up and taken it home. We need to speak to that person or anyone who has seen it."
Officers said they have received "hundreds" of calls about the case and investigators are trying to establish a timeline of events.
They said a “location of interest" was identified after the investigation led them to a spot on Scenic Drive, a country road about 12 miles west of the city centre, on Saturday night.
Mr Beard said investigators had "located a body which we believe to be Grace" about 30 feet from the roadside.
The last confirmed sighting of the University of Lincoln graduate Grace was at 9.41pm on December 1, the day before her birthday, at the Citylife Hotel, when she was seen with a "male companion".
Since arriving in New Zealand from Peru on November 20, she had been in near-daily contact with her family in Essex.
Police received a missing person report on Wednesday and began a major search as well as a public campaign that saw dozens of calls made to a helpline.
Grace’s father, David Millane, flew to Auckland and made a public appeal for help finding his daughter, who he described as "lovely, outgoing, fun-loving (and) family-orientated".
Her brother, Declan Millane, paid tribute by sharing pictures on social media of him and his sister, adding the lyrics of You Are My Sunshine.
He wrote on Instagram: "You are my sunshine, my only sunshine. You make me happy when skies are gray. You'll never know, dear, how much I love you. Please don't take my sunshine away.
New Zealand's prime minister Jacinda Ardern gave an emotional apology to Grace's family, saying: "Your daughter should have been safe here, and she wasn't, and I'm sorry for that."
"I cannot imagine the grief of her family and what they would be experiencing and feeling right now."
It has emerged the man accused of the murder was due to go on a Tinder date on the night Grace was murder but cancelled it.
He is reported to have dated a number of Brit backpackers and liked “the admiration of young females”.
Criminologist Greg Newbold said the suspect, who has not applied for bail, is likely to be the target violence in prison.
"At the moment he'll be public enemy number one … but you have to remember he hasn't been tried yet."
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